Pearson, Spearman and Kendall correlation
Pearson measures linear association, Spearman uses midranks and Kendall uses tau-b.
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Pearson measures linear association, Spearman uses midranks and Kendall uses tau-b. None of them proves causality. The p-value uses a t approximation for Pearson and Spearman, and a tie-corrected normal approximation for Kendall. The Pearson Fisher-z interval needs n > 3. The paired, seeded percentile bootstrap visibly omits undefined resamples and needs at least 80% valid ones. Use up to 1000 pairs, or 200 for Kendall. For n = 2, Pearson p is 1, and rank p-values and bootstrap intervals are unavailable.
Model, grammar and limits
r=Σdx·dy/√(Σdx²Σdy²); ρ=cor(rank x,rank y); τᵦ=(C−D)/√[(N−Tₓ)(N−Tᵧ)]
Limits: 256000 raw data characters, 5000 source records and 50000 cells in total; decimals up to 48 characters; up to 20 groups or contributions and 50 columns. Limits for exact and bootstrap methods are stated with each tool. Parsing and resource checks run before the calculation, and the worker stops after 15 seconds. Editing, canceling or resetting discards pending results.
Check assumptions, ties and missing values before drawing conclusions. Results show 10 significant digits; CSV keeps the numeric values and units. Exact enumeration means exact counts, not exact displayed decimals. Numerical tail zeros, floors and unavailable intervals are labeled. Nothing here is a diagnosis, proof of causation or validity approval.
Your data stays in this browser. The calculation runs in a local worker, and CSV and backup files are local downloads you choose to make. Your data is not sent anywhere or saved silently, so keep your original data. Input data, formulas and filenames are never sent. Only with your optional consent, Refentra sends aggregate counts of actions and outcomes, without input content.
Use the chosen model
- Model, grammar and limits
Pearson measures linear association, Spearman uses midranks and Kendall uses tau-b. None of them proves causality. The p-value uses a t approximation for Pearson and Spearman, and a tie-corrected normal approximation for Kendall. The Pearson Fisher-z interval needs n > 3. The paired, seeded percentile bootstrap visibly omits undefined resamples and needs at least 80% valid ones. Use up to 1000 pairs, or 200 for Kendall. For n = 2, Pearson p is 1, and rank p-values and bootstrap intervals are unavailable.
- Calculate
r=Σdx·dy/√(Σdx²Σdy²); ρ=cor(rank x,rank y); τᵦ=(C−D)/√[(N−Tₓ)(N−Tᵧ)]. Limits: 256000 raw data characters, 5000 source records and 50000 cells in total; decimals up to 48 characters; up to 20 groups or contributions and 50 columns. Limits for exact and bootstrap methods are stated with each tool. Parsing and resource checks run before the calculation, and the worker stops after 15 seconds. Editing, canceling or resetting discards pending results.
- Download CSV report
Check assumptions, ties and missing values before drawing conclusions. Results show 10 significant digits; CSV keeps the numeric values and units. Exact enumeration means exact counts, not exact displayed decimals. Numerical tail zeros, floors and unavailable intervals are labeled. Nothing here is a diagnosis, proof of causation or validity approval. Your data stays in this browser. The calculation runs in a local worker, and CSV and backup files are local downloads you choose to make. Your data is not sent anywhere or saved silently, so keep your original data. Input data, formulas and filenames are never sent. Only with your optional consent, Refentra sends aggregate counts of actions and outcomes, without input content.
Model questions
Model, grammar and limits
Pearson measures linear association, Spearman uses midranks and Kendall uses tau-b. None of them proves causality. The p-value uses a t approximation for Pearson and Spearman, and a tie-corrected normal approximation for Kendall. The Pearson Fisher-z interval needs n > 3. The paired, seeded percentile bootstrap visibly omits undefined resamples and needs at least 80% valid ones. Use up to 1000 pairs, or 200 for Kendall. For n = 2, Pearson p is 1, and rank p-values and bootstrap intervals are unavailable. r=Σdx·dy/√(Σdx²Σdy²); ρ=cor(rank x,rank y); τᵦ=(C−D)/√[(N−Tₓ)(N−Tᵧ)]
Unit
Paired columns x, y; Correlation coefficient; Correlation interval profile; Confidence level, fraction (1); Bootstrap repetitions (1); Reproducible seed (1); Missing-data policy; x measurement unit; y measurement unit. Limits: 256000 raw data characters, 5000 source records and 50000 cells in total; decimals up to 48 characters; up to 20 groups or contributions and 50 columns. Limits for exact and bootstrap methods are stated with each tool. Parsing and resource checks run before the calculation, and the worker stops after 15 seconds. Editing, canceling or resetting discards pending results.
Model results
Check assumptions, ties and missing values before drawing conclusions. Results show 10 significant digits; CSV keeps the numeric values and units. Exact enumeration means exact counts, not exact displayed decimals. Numerical tail zeros, floors and unavailable intervals are labeled. Nothing here is a diagnosis, proof of causation or validity approval.
Download input backup
Your data stays in this browser. The calculation runs in a local worker, and CSV and backup files are local downloads you choose to make. Your data is not sent anywhere or saved silently, so keep your original data. Input data, formulas and filenames are never sent. Only with your optional consent, Refentra sends aggregate counts of actions and outcomes, without input content.